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- Woodall_number abstract "In number theory, a Woodall number (Wn) is any natural number of the form for some natural number n. The first few Woodall numbers are: 1, 7, 23, 63, 159, 383, 895, … (sequence A003261 in OEIS).Woodall numbers were first studied by Allan J. C. Cunningham and H. J. Woodall in 1917, inspired by James Cullen's earlier study of the similarly-defined Cullen numbers. Woodall numbers curiously arise in Goodstein's theorem.[citation needed]Woodall numbers that are also prime numbers are called Woodall primes; the first few exponents n for which the corresponding Woodall numbers Wn are prime are 2, 3, 6, 30, 75, 81, 115, 123, 249, 362, 384, … (sequence A002234 in OEIS); the Woodall primes themselves begin with 7, 23, 383, 32212254719, … (sequence A050918 in OEIS).In 1976 Christopher Hooley showed that almost all Cullen numbers are composite.[citation needed] Hooley's proof was reworked by Hiromi Suyama to show that it works for any sequence of numbers n · 2n+a + b where a and b are integers,[citation needed] and in particular also for Woodall numbers. Nonetheless, it is conjectured that there are infinitely many Woodall primes.[citation needed] As of December 2007, the largest known Woodall prime is 3752948 × 23752948 − 1. It has 1,129,757 digits and was found by Matthew J. Thompson in 2007 in the distributed computing project PrimeGrid.Like Cullen numbers, Woodall numbers have many divisibility properties. For example, if p is a prime number, then p dividesW(p + 1) / 2 if the Jacobi symbol is +1 andW(3p − 1) / 2 if the Jacobi symbol is −1.[citation needed]A generalized Woodall number is defined to be a number of the form n × bn − 1, where n + 2 > b; if a prime can be written in this form, it is then called a generalized Woodall prime.".
- Woodall_number wikiPageExternalLink GeneralizedWoodallPrimes.txt.
- Woodall_number wikiPageExternalLink page.php?sort=WoodallNumber.
- Woodall_number wikiPageExternalLink page.php?id=7.
- Woodall_number wikiPageExternalLink S0025-5718-1995-1308456-3.pdf.
- Woodall_number wikiPageExternalLink cw.html.
- Woodall_number wikiPageID "321962".
- Woodall_number wikiPageRevisionID "603966204".
- Woodall_number hasPhotoCollection Woodall_number.
- Woodall_number title "Woodall number".
- Woodall_number urlname "WoodallNumber".
- Woodall_number subject Category:Integer_sequences.
- Woodall_number subject Category:Unsolved_problems_in_mathematics.
- Woodall_number type Abstraction100002137.
- Woodall_number type Arrangement107938773.
- Woodall_number type Attribute100024264.
- Woodall_number type Condition113920835.
- Woodall_number type Difficulty114408086.
- Woodall_number type Group100031264.
- Woodall_number type IntegerSequences.
- Woodall_number type Ordering108456993.
- Woodall_number type Problem114410605.
- Woodall_number type Sequence108459252.
- Woodall_number type Series108457976.
- Woodall_number type State100024720.
- Woodall_number type UnsolvedProblemsInMathematics.
- Woodall_number comment "In number theory, a Woodall number (Wn) is any natural number of the form for some natural number n. The first few Woodall numbers are: 1, 7, 23, 63, 159, 383, 895, … (sequence A003261 in OEIS).Woodall numbers were first studied by Allan J. C. Cunningham and H. J. Woodall in 1917, inspired by James Cullen's earlier study of the similarly-defined Cullen numbers.".
- Woodall_number label "Nombre de Woodall".
- Woodall_number label "Numero di Woodall".
- Woodall_number label "Número de Woodall".
- Woodall_number label "Número de Woodall".
- Woodall_number label "Woodall number".
- Woodall_number label "Woodallgetal".
- Woodall_number label "Число Вудала".
- Woodall_number label "胡道爾數".
- Woodall_number sameAs Número_de_Woodall.
- Woodall_number sameAs Nombre_de_Woodall.
- Woodall_number sameAs Numero_di_Woodall.
- Woodall_number sameAs Woodallgetal.
- Woodall_number sameAs Número_de_Woodall.
- Woodall_number sameAs m.01vmmc.
- Woodall_number sameAs Q951293.
- Woodall_number sameAs Q951293.
- Woodall_number sameAs Woodall_number.
- Woodall_number wasDerivedFrom Woodall_number?oldid=603966204.
- Woodall_number isPrimaryTopicOf Woodall_number.